Is \theta_{13}^{PMNS} correlated with \theta_{23}^{PMNS} or not?

TL;DR

This paper investigates whether the neutrino mixing angle _{23} is correlated with _{13} by analyzing a proposed relation, exploring its origins, and examining experimental data and theoretical conditions for such a correlation.

Contribution

It introduces a general condition for the _{23} and _{13} relation, analyzes its dependence on neutrino parameters, and discusses possible origins from flavor symmetries or radiative corrections.

Findings

Global data favor _{23}  _{13} relation with ta=\u00b1 1/

T2K and Super-Kamiokande data prefer ta=0, indicating near maximal _{23}

Correction terms can originate from flavor symmetries or radiative effects

Abstract

By postulating the relation \theta_{23} \simeq 45^\circ + \eta\theta_{13}, we seek preferable correction terms to tri-bi-maximal mixing and discuss their origins. Global analyses of the neutrino oscillation parameters favor \eta=\pm 1/\sqrt{2}; this corresponds to the relation found by Edy, Frampton, and Matsuzaki some years ago in the context of a T^\prime flavor symmetry. In contrast, the results of the \nu_\mu disappearance mode reported by the T2K and Super-Kamiokande collaborations seem to prefer \eta=0, which gives an almost maximal \theta_{23}. We derive a general condition for ensuring \theta_{23} \simeq 45^\circ + \eta\theta_{13} and find that the condition is complicated by the neutrino masses and CP violating phases. We investigate the condition under simplified environments and arrive at several correction terms to the mass matrices. It is found that the obtained correction terms can arise from flavor symmetries or one-loop radiative corrections.